Cole and Luke started on a 50-km cycling trip at the same time. They cycled at the same speed for first 10 km. For the remaining 40 km, Cole cycled faster than Luke. He arrived at the finishing point 40 minutes before Luke who was 10 km behind him. Luke did not change his speed throughout and completed it at 07 30.

1. At what time did the trip begin? Give the answer in 12-hour format.
2. What was Cole's average speed for the remaining 40 km of the trip in km/h?

(a)
60 min = 1 h
40 min =⁴⁰₆₀ h = ²₃ 

Luke's average speed
= 10 ÷ ²₃
= 15 km/h

Time that Luke took for the trip
= 50 ÷ 15
= 3⁵₁₅ h
= 3¹₃ h
= 3 h 20 min

3 h 20 min before 07 30 is 04 10.

(b)
To find the time that Cole took for the remaining 40 km of the trip, we need to use the time that Luke took subtract that of the time taken for first 10 km and the time that Cole was faster than Luke.

Time that Cole took for the remaining 40 km of the trip
= 3¹₃ - ²₃ - ²₃
= 2 h

Cole's average speed
= 40 ÷ 2
= 20 km/h

Answer(s): (a) 04 10; (b) 20 km/h